The purpose of the article: to find new (most effective) directions for the corporate COVID-19 risks management and developing management implications for leading this fight amid the pandemic and crisis for sustainable development. The methods of correlation and regression analysis are used. It is proved that the most perspective method of the corporate fight against the COVID-19 risks is a flexible transformation of business according to the new conditions based on the Industry 4.0 technologies. This paper further develops and supplements the concept of corporate social responsibility, including a new direction—corporate fight against the COVID-19 risks in it. The authors develop management implications on improving the corporate fight against the COVID-19 risks as a new direction of corporate social responsibility amid the pandemic. The advantages of using the Industry 4.0 technologies for the corporate fight against the viral threat include reduction of the share of the population with household expenditures for healthcare above 25% of total expenditures or incomes, reduction of the number of new cases per 1 million people, and an increase of the self-isolation index, the share of responsible employers amid COVID-19 risks.